Digital Textbook & Academic Curriculum

Engineering Mechanics:
Statics

A rigorous digital curriculum and computational platform designed for engineering students, educators, and structural analysts. Master particle equilibrium, rigid body mechanics, structural trusses, and internal beam forces through analytical theory and structured coursework.

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Governing Equations & Statics
$$\sum \mathbf{F} = \mathbf{0} \implies \begin{cases} \sum F_x = 0 \\ \sum F_y = 0 \\ \sum F_z = 0 \end{cases}$$
$$\sum \mathbf{M}_O = \sum (\mathbf{r} \times \mathbf{F}) = \mathbf{0}$$
A (Pin) B (Roller) P w(x)

Engineering Mechanics: Statics Chapters

Structured according to global engineering accreditation standards. Each chapter combines analytical theory, derivations, free-body diagrams, and interactive web tools.

CHAPTER 01

General Principles & Vector Mechanics

Fundamentals of Newtonian mechanics, coordinate transformations, Cartesian vectors, and dot products.

$$\mathbf{F} = F_x \mathbf{i} + F_y \mathbf{j} + F_z \mathbf{k}$$
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CHAPTER 02

Equilibrium of a Particle

Coplanar and three-dimensional force systems, free-body diagrams (FBD), and concurrent forces.

$$\sum \mathbf{F} = \mathbf{0} \iff \sum F_x = 0, \, \sum F_y = 0, \, \sum F_z = 0$$
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CHAPTER 03

Force System Resultants & Moments

Vector cross products, moment of a force about a point and axis, couple moments, and equivalent systems.

$$\mathbf{M}_O = \mathbf{r} \times \mathbf{F} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ r_x & r_y & r_z \\ F_x & F_y & F_z \end{vmatrix}$$
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CHAPTER 04

Equilibrium of a Rigid Body

Support reactions in 2D and 3D, constraints, static determinacy, and complete equilibrium conditions.

$$\sum \mathbf{F} = \mathbf{0}, \quad \sum \mathbf{M}_O = \mathbf{0}$$
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CHAPTER 05

Centroids, Center of Gravity & Distributed Loads

Centroids of lines, composite areas, cutouts, 3D volumes, and distributed surface loads.

$$\bar{x} = \frac{\sum \tilde{x} A}{\sum A}, \quad \bar{y} = \frac{\sum \tilde{y} A}{\sum A}$$
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CHAPTER 06

Structural Analysis: Trusses, Frames & Machines

Planar trusses, Method of Joints, Method of Sections, zero-force members, and multi-force member systems.

$$2j = m + r \quad \text{(Statical Determinacy)}$$
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CHAPTER 07

Internal Forces: Shear Force & Bending Moment

Normal force, shear force, and bending moment diagrams for statically determinate beam configurations.

$$\frac{dV}{dx} = -w(x), \quad \frac{dM}{dx} = V(x)$$
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CHAPTER 08

Friction & Dry Contact Mechanics

Coulomb friction laws, angle of friction, wedges, belt friction, and screws under impending motion.

$$F_{\text{max}} = \mu_s N, \quad T_2 = T_1 e^{\mu \beta}$$
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CHAPTER 09

Moments of Inertia & Mohr's Circle

Second moments of area, radius of gyration, parallel-axis theorem, and principal axes.

$$I_x = \int y^2 \, dA, \quad I = \bar{I} + A d^2$$
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CHAPTER 10

Deflection of Determinate Structures by Virtual Work

Principle of virtual work, virtual displacements, degree of freedom, and deflection of complex structures.

$$1 \cdot \Delta = \sum \frac{n N L}{A E} + \int \frac{m M}{E I} \, dx$$
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